Question: $89$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $111$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 89}$ ${x = 4y-111}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-111}$ for $x$ in the first equation. ${(4y-111)}{+ y = 89}$ Simplify and solve for $y$ $ 4y-111 + y = 89 $ $ 5y-111 = 89 $ $ 5y = 200 $ $ y = \dfrac{200}{5} $ ${y = 40}$ Now that you know ${y = 40}$ , plug it back into ${x = 4y-111}$ to find $x$ ${x = 4}{(40)}{ - 111}$ $x = 160 - 111$ ${x = 49}$ You can also plug ${y = 40}$ into ${x+y = 89}$ and get the same answer for $x$ ${x + }{(40)}{= 89}$ ${x = 49}$ There were $49$ home team fans and $40$ away team fans.